How do I make a square when the existing edge is not alined to any of the axes?
With the edge selected open up the properties pane with N Scroll down to the Mesh display section and turn on Length for the Edge Info. 

Now press E to extrude, then press YY to constrain the movement to the Y Normal axis. Pressing XX or ZZ would lock movement to each their respective axes. Finally before you confirm the movement, type in the length of the first edge.